Choosing between Concentration Indices: The Iso-Concentration Curve

It is usual to identify two constituent parts to concentration in any industry: n, the number of firms in that industry and I, the inequalities in the market shares of those firms. For instance, in the conventional structure-conduct-performance models relating industry profitability to the potential for collusion, it is usually argued that collusion (and a number of other non-competitive regimes, e.g. price leadership) should be easier to achieve and sustain, the fewer firms there are in the industry and, for a given number of firms, the more disproportionately large is the share of the leading firms. In the literature concerning the most appropriate empirical index of concentration, much of the argument has centred on the relative weights that should be attached to these two constituents. Thus Phillips (1976, p. 242), along with many others, has criticized the concentration ratio (CR) because it ignores size inequalities within the leading group of firms (which itself is arbitrarily defined) and emphasizes only the inequalities between the leading group and all other firms. Similarly, he claims the relationship between CR and firm numbers (n) is variable and ambiguous. The various indices derived from the Lorenz Curve (L) overcome some of these problems; being based on the entire cumulative concentration curve, they reflect I fairly unambiguously. This is achieved, however, only at the cost of virtually ignoring firm numbers-an industry of 100 equally sized firms will record the same value for L (as defined in Table 1) as one of five equally sized firms. Initially it was supposed that the Herfindahl index (H) and other similar indices1 overcame these problems in that they reflected both I and n. Subsequently, however, Hart has suggested that H is too sensitive to n and that, therefore, CR may be preferable.2 Phillips, on the other hand, has questioned whether the weighting attached to I is appropriate (1976, pp. 242-243). In recent years, the various entropy statistics, arising out of information theory, have become increasingly popular. While these have been subject to less critical attention by most economists, Hart (1975, p. 427) notes that the firstorder entropy (E) may suffer from its clear dependence on n. There are, of course, many other indices suggested in the literature, although mostly they may be seen as variations on one or other of the four basic types